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arXiv · 1310.1520

Number of cycles in the graph of 312-avoiding permutations

Richard Ehrenborg·Sergey Kitaev·Einar Steingrimsson
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Abstract

The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. That is, for every permutation $π= π_{1} π_{2} ... π_{n+1}$ there is a directed edge from the standardization of $π_{1} π_{2} ... π_{n}$ to the standardization of $π_{2} π_{3} ... π_{n+1}$. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping 312-avoiding permutations. Using this we also give a refinement of the enumeration of 312-avoiding affine permutations and point out some open problems on this graph, which so far has been little studied.

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Richard Ehrenborg, Sergey Kitaev, Einar Steingrimsson. 2014-09-16. Number of cycles in the graph of 312-avoiding permutations. https://doi.org/10.1016/j.jcta.2014.09.004

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